Can I see tasks on a board, calendar, or Gantt timeline?

Yes. The same tasks appear in five views — Board (drag-and-drop Kanban), List, Calendar (by due date), Table (with inline editing), and a Timeline/Gantt that draws each task as a start-to-due bar. Switch views from the tab bar at the top of the Tasks page; the data is one source, so a change in one view shows up in all of them.